Polymeric strapping is extensively used in conjunction with tie heads to anchor bundles of objects, such as utility wires and lengths of rod or pipe. Fastening systems previously developed for such applications typically included a tie head through which a strapping material was inserted, the head including barbs or clipping means for retaining the strap in the tie head. Continuing effort has been directed toward the improvement of such systems, and particularly the efficiency and reliability of such tie heads and their combination with specific strapping materials.